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Cash flow analysis - Exam FM formula sheet

Every Exam FM formula in cash flow analysis on one printable sheet, condensed from the 4 reference pages that teach them.

4 topics, 13 formula lines. Every line is condensed from the Exam FM formula pages, which stay free to read in full. Print this page to get the sheet on paper; the site chrome drops away.

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Cash flow analysis

Net present value

NPV: $NP V (i) = \sum_{t \geq 0} C_{t} v^{t}$
Decision rule: $NP V (i) > 0 \Rightarrow accept at required return i$
NPV is decreasing: $\frac{d}{d i} NP V (i) < 0$ for a conventional project

IRR

Definition: $NP V (i^{*}) = \sum_{t \geq 0} C_{t} (1 + i^{*})^{- t} = 0$
Descartes' bound: $# sign changes \geq # positive roots$
Dollar-weighted (simple interest approximation): $i \approx \frac{I}{A + \sum _{t} C _{t} ( 1 - t )}$
Time-weighted: $1 + i = \prod_{k} \frac{B _{k}}{B _{k - 1} + C _{k - 1}}$

Spot rates

Present value: $P V = \sum_{t} \frac{C _{t}}{( 1 + s _{t} ) ^{t}}$
Zero-coupon price: $P (t) = (1 + s_{t})^{- t}$
Par yield: $\sum_{t = 1}^{n} \frac{c}{( 1 + s _{t} ) ^{t}} + \frac{1}{( 1 + s _{n} ) ^{n}} = 1$ solve for the coupon c that prices at par

Forward rates

Implied forward: $(1 + s_{t_{2}})^{t_{2}} = (1 + s_{t_{1}})^{t_{1}} (1 + f_{t_{1}, t_{2}})^{t_{2} - t_{1}}$
One-period forward: $1 + f_{t, t + 1} = \frac{( 1 + s _{t + 1} ) ^{t + 1}}{( 1 + s _{t} ) ^{t}}$
Spot as a geometric mean: $(1 + s_{n})^{n} = \prod_{t = 0}^{n - 1} (1 + f_{t, t + 1})$

Cash flow analysis - Exam FM formula sheet. Formulas condensed from the free reference pages on this site. Not affiliated with or endorsed by the Society of Actuaries.